May I suggest another solution?
As the search db and the history db only really make sense for a specific computer, why not just append '%ComputerName%' to the corresponding file names?
This way the preferences could stay the same for all computers (in contrary to having multiple 'UserData' folders). Dropbox users just have to make sure their computers actually have different names, and other users won't be bothered at all.
Additionally (or as an alternative to the above) I think a couple of users would appreciate to not store the search db and/or the history db to disk at all (slow writing speeds on USB drives, limited storage on cloud service, security concerns, etc.). E.g. by two check boxes 'Purge search db on exit?' and 'Purge history on exit?'.
For your consideration.